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Turbulent Entrainment in Weak Fountains<br />
G. R. Hunt ∗ and N. B. Kaye ∗<br />
Abstract<br />
We determine analytically the initial rise height zm of turbulent Boussinesq<br />
fountains for small and large source Froude numbers Fr0. Our model uses<br />
a recasting of the plume conservations equations of Morton, Taylor & Turner<br />
(1956) in terms of the Richardson number (inverse square of Fr0) and a local<br />
dimensionless fountain width. For highly-forced fountains (large Fr0) the wellestablished<br />
linear increase of the rise height with Fr0 is obtained, i.e. zm/r0 ∼<br />
Fr0; r0 denoting the source radius. In contrast, for small Fr0 the fountain is<br />
‘weak’ and the dependence zm/r0 ∼ Fr 2 0 is predicted.<br />
Experiments were conducted to establish the nature of the entrainment and<br />
rise height on the source Froude number. Based on our experiments and analytical<br />
solution we find that αf ≈ 0.058 which is significantly closer to that of<br />
a jet than of a plume. We discuss this result in the context of existing variable<br />
entrainment models.<br />
Morton, B. R., Taylor, G. I. & Turner, J. S. (1956), Turbulent gravitational<br />
convection from maintained and instantaneous sources, Proc. Roy. Soc. A 234,<br />
123.<br />
∗ Imperial College London, London, UK.<br />
95
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